Exploring the fundamental limits of integrated beam splitters with arbitrary phase via topology optimization

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Original languageEnglish
Pages (from-to)1125-1128
Number of pages4
JournalOptics letters
Volume49
Issue number5
Publication statusPublished - 20 Feb 2024

Abstract

Optical beam splitters are essential for classical and quantum photonic on-chip systems. In integrated optical technology, a beam splitter can be implemented as a beam coupler with two input and two output ports. The output phases are constrained by the conservation of energy. In lossless beam splitters, the phase shift between the output fields is π and zero for excitation from the first and second input ports, respectively. Therefore, for excitation from both inputs, the phase between the output fields, defined as beam splitter phase (BSP), is π. The BSP leads to several phenomena, such as the quantum interference between two photons, known as the Hong–Ou–Mandel effect. By introducing losses, BSP values different than π become theoretically possible, but the design of 2 × 2 beam couplers with an arbitrary phase is elusive in integrated optics. Inspired by the growing interest on fundamental limits in electromagnetics and inverse design, here we explore the theoretical limits of symmetrical integrated beam splitters with an arbitrary BSP via adjoint-based topology optimization. Optimized 2D designs accounting for fabrication constraints are obtained for several combinations of loss and phase within the theoretical design space. Interestingly, the algorithm does not converge for objectives outside of the theoretical limits. Designs of beam splitters with arbitrary phase may find use in integrated optics for quantum information processing.

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Exploring the fundamental limits of integrated beam splitters with arbitrary phase via topology optimization. / Nanda, Abhishek; Kues, Michael; Lesina, Antonio Calà.
In: Optics letters, Vol. 49, No. 5, 20.02.2024, p. 1125-1128.

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title = "Exploring the fundamental limits of integrated beam splitters with arbitrary phase via topology optimization",
abstract = "Optical beam splitters are essential for classical and quantum photonic on-chip systems. In integrated optical technology, a beam splitter can be implemented as a beam coupler with two input and two output ports. The output phases are constrained by the conservation of energy. In lossless beam splitters, the phase shift between the output fields is π and zero for excitation from the first and second input ports, respectively. Therefore, for excitation from both inputs, the phase between the output fields, defined as beam splitter phase (BSP), is π. The BSP leads to several phenomena, such as the quantum interference between two photons, known as the Hong–Ou–Mandel effect. By introducing losses, BSP values different than π become theoretically possible, but the design of 2 × 2 beam couplers with an arbitrary phase is elusive in integrated optics. Inspired by the growing interest on fundamental limits in electromagnetics and inverse design, here we explore the theoretical limits of symmetrical integrated beam splitters with an arbitrary BSP via adjoint-based topology optimization. Optimized 2D designs accounting for fabrication constraints are obtained for several combinations of loss and phase within the theoretical design space. Interestingly, the algorithm does not converge for objectives outside of the theoretical limits. Designs of beam splitters with arbitrary phase may find use in integrated optics for quantum information processing.",
author = "Abhishek Nanda and Michael Kues and Lesina, {Antonio Cal{\`a}}",
note = "Funding Information: Funding. European Research Council (QFreC project, Grant agreement ID 947603); Deutsche Forschungsgemeinschaft (EXC 2122, Project ID 390833453). Simulations were performed, in part, on the central computing cluster operated by Leibniz University IT Services (LUIS), which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project number INST 187/742-1 FUGG. We also acknowledge the computing time granted by the Resource Allocation Board and provided on the supercomputer Lise and Emmy at NHR@ZIB and NHR@G{\"o}ttingen as part of the NHR infrastructure (calculations were conducted with computing resources under the project nip00059). ",
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T1 - Exploring the fundamental limits of integrated beam splitters with arbitrary phase via topology optimization

AU - Nanda, Abhishek

AU - Kues, Michael

AU - Lesina, Antonio Calà

N1 - Funding Information: Funding. European Research Council (QFreC project, Grant agreement ID 947603); Deutsche Forschungsgemeinschaft (EXC 2122, Project ID 390833453). Simulations were performed, in part, on the central computing cluster operated by Leibniz University IT Services (LUIS), which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project number INST 187/742-1 FUGG. We also acknowledge the computing time granted by the Resource Allocation Board and provided on the supercomputer Lise and Emmy at NHR@ZIB and NHR@Göttingen as part of the NHR infrastructure (calculations were conducted with computing resources under the project nip00059).

PY - 2024/2/20

Y1 - 2024/2/20

N2 - Optical beam splitters are essential for classical and quantum photonic on-chip systems. In integrated optical technology, a beam splitter can be implemented as a beam coupler with two input and two output ports. The output phases are constrained by the conservation of energy. In lossless beam splitters, the phase shift between the output fields is π and zero for excitation from the first and second input ports, respectively. Therefore, for excitation from both inputs, the phase between the output fields, defined as beam splitter phase (BSP), is π. The BSP leads to several phenomena, such as the quantum interference between two photons, known as the Hong–Ou–Mandel effect. By introducing losses, BSP values different than π become theoretically possible, but the design of 2 × 2 beam couplers with an arbitrary phase is elusive in integrated optics. Inspired by the growing interest on fundamental limits in electromagnetics and inverse design, here we explore the theoretical limits of symmetrical integrated beam splitters with an arbitrary BSP via adjoint-based topology optimization. Optimized 2D designs accounting for fabrication constraints are obtained for several combinations of loss and phase within the theoretical design space. Interestingly, the algorithm does not converge for objectives outside of the theoretical limits. Designs of beam splitters with arbitrary phase may find use in integrated optics for quantum information processing.

AB - Optical beam splitters are essential for classical and quantum photonic on-chip systems. In integrated optical technology, a beam splitter can be implemented as a beam coupler with two input and two output ports. The output phases are constrained by the conservation of energy. In lossless beam splitters, the phase shift between the output fields is π and zero for excitation from the first and second input ports, respectively. Therefore, for excitation from both inputs, the phase between the output fields, defined as beam splitter phase (BSP), is π. The BSP leads to several phenomena, such as the quantum interference between two photons, known as the Hong–Ou–Mandel effect. By introducing losses, BSP values different than π become theoretically possible, but the design of 2 × 2 beam couplers with an arbitrary phase is elusive in integrated optics. Inspired by the growing interest on fundamental limits in electromagnetics and inverse design, here we explore the theoretical limits of symmetrical integrated beam splitters with an arbitrary BSP via adjoint-based topology optimization. Optimized 2D designs accounting for fabrication constraints are obtained for several combinations of loss and phase within the theoretical design space. Interestingly, the algorithm does not converge for objectives outside of the theoretical limits. Designs of beam splitters with arbitrary phase may find use in integrated optics for quantum information processing.

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DO - 10.1364/OL.512100

M3 - Letter

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AN - SCOPUS:85186318650

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SP - 1125

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JO - Optics letters

JF - Optics letters

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ER -

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